Asymptotic Analysis - Volume 4, issue 4

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ISSN 0921-7134 (P)
ISSN 1875-8576 (E)

Impact Factor 2018: 0.748

The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand.

Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.

Abstract: This paper deals with mathematical properties of the semiconductor Boltzmann equation. We first investigate the question of existence of solutions and some basic properties of the collision operator. Then we study the connection with the drift diffusion model by using a perturbation approach, the so-called diffusion approximation. For justifying rigorously this theory, we have to deal with boundary layers. A half space problem (Milne problem) arises in the study of the boundary corrector. We prove existence and we give the asymptotic behaviour of its solutions.

Abstract: A mathematical modeling of the junction between three-dimensional and two-dimensional linearly elastic structures has been recently proposed by P.G. Ciarlet, H. le Dret and R. Nzengwa. Their approach is generalized here to nonlinear elastic structures.

Abstract: We describe a construction, based on variational inequalities, which gives a hierarchy of upper and lower bounds (of odd orders 2k+1), on the various effective moduli of random multiphase materials and polycrystals. The bounds of order 2k+1 on a given effective modulus can be explicitly evaluated if a truncated Taylor expansion of the given modulus is known to order 2k+1. Our approach is motivated by prior investigations of Beran and other authors. Our calculations do not involve Green functions or n-point correlation functions, and they are very simple. We thus rederive known and obtain new sequences of bounds on the…different effective moduli. We also describe a method that, for cell materials (i.e. materials in which cells of smaller and smaller length scales cover all space, with material properties assigned at random), permits one to calculate the truncated Taylor expansions that are needed for the explicit evaluation of the bounds. In connection with this, we show that the first coefficient in the low volume fraction expansion of any effective modulus of a cell material, coincides with the corresponding low volume fraction coefficient for an array of cells randomly distributed in a matrix.
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Abstract: We study the behavior of positive solutions of semilinear elliptic equations −div(aε (x)Duε =g(uε ) with homogeneous Dirichlet boundary data, with respect to the G-convergence of the elliptic matrices aε . Here the function g has a subcritical or critical growth with respect to Sobolev imbedding.